Non-Fermi liquid behavior in a mixed valent metallic pyrochlore iridate Pb$_2$Ir$_2$O$_{7-\delta}$

Non-Fermi liquid behavior in some fermionic systems have attracted significant interest in last few decades. Certain pyrochlore iridates with stronger spin-orbit coupling strength have recently been added to the list. Here, we provide evidence of such a non-Fermi liquid ground state in another mixed valent metallic pyrochlore iridate Pb$_2$Ir$_2$O$_{7-\delta}$, through the combined investigation of electronic, magnetic and thermodynamic properties as a function of temperature ($T$) and applied magnetic field ($H$). Resistivity measurement showed a linear temperature dependence down to 15~K below which it shows $\rho \sim T^{3/2}$ dependence while magnetic susceptibility diverges as $\chi$(T) $\sim$ $T^{-\alpha}$ ($\alpha < 1$) below 10~K. While a strong negative $\Theta_{CW}$ has been observed from Curie-Weiss fitting, absence of any long range order down to 80~mK only indicates presence of strong inherent geometric frustration in the system. Heat capacity data showed $C_p$ $\sim$ $T\ln(T_0/T)$ + ${\beta}T^3$ dependence below 15~K down to 1.8~K. More importantly spin-orbit coupling strength by x-ray absorption spectroscopy was found to be weaker in Pb$_2$Ir$_2$O$_{7-\delta}$ compared to other pyrochlore iridates. In absence of any large moment rare earth magnetic ion, Pb$_2$Ir$_2$O$_{7-\delta}$ presents a rare example of an irirdate system showing non-Fermi liquid behaviour due to disordered distribution of Ir$^{4+}$ and Ir$^{5+}$ having markedly different strengths of spin-orbit coupling which might offer a prescription for achieving new non-Fermi liquid systems.